Pat the lamb dry and season it with salt and black pepper. Heat the olive oil in a Dutch oven over medium heat, then brown the lamb in batches until all sides are seared. Remove the meat and set it aside.

Add the onion and carrots to the same pot. Cook for 5 minutes until the onion softens. Stir in the garlic and tomato paste and cook for 1 minute more.

Pour in the stout beer and scrape the bottom to loosen any browned bits. Return the lamb to the pot along with the beef broth, thyme sprigs, and bay leaf. Bring to a simmer, then cover and cook on low for 1 hour and 30 minutes until the lamb is tender.

While the stew simmers, make the dumplings. In a bowl, mix the flour, baking powder, parsley, dried thyme, and 0.5 teaspoon salt. Cut in the cold butter until the mixture looks like coarse crumbs, then stir in the milk just until a soft dough forms.

Drop spoonfuls of the dumpling dough onto the surface of the simmering stew. Cover the pot and cook for 15 minutes without lifting the lid until the dumplings are firm and cooked through. Remove the thyme sprigs and bay leaf before serving.